What we have discussed so far falls within the realm of information design or Bayesian persuasion with privately informed receiver [1]}, [2]}, where the leader already acquires enough information, including possible follower's types as well as the prior distribution \(\mu ^*\) , to compute the sigBSE offline. However, in reality, the leader may not even know the prior distribution (an ignorant leader), and hence she has to learn a signaling commitment with a satisfying online performance. In this section, we aim to provide an online learning framework that enables the leader to adaptively adjust her signaling commitment based on her past experience, and we show that the proposed learning method guarantees that the online performance of the learned commitment is comparable to the equilibrium payoff under sigBSE, the optimal expected utility.
